In U.S. Pat. No. 3,799,039 issued Mar. 26, 1974 to George R. Johnson and entitled "Cushioning Dunnage Mechanism and Method" there is disclosed a cushioning dunnage producing mechanism of the general type of the present invention. While such prior art mechanism represented a considerable improvement over previous prior art arrangements for producing cushioning dunnage, there were still problems involved in the use of the machine illustrated in such patent. One of the problems was the tendency of the sheet-like stock material to tear during the dunnage producing operation and during its movement from a composite roll of the stock material into the crumpler section of the machine. Tearing of the stock material generally necessitated shutting down of the machine and reinserting non-torn portions of the webs from the stock roll into the crumpler mechanism, so that a high quality dunnage pad could be produced in the mechanism. Moreover, with the arrangement disclosed in the U.S. Pat. No. 3,799,039, the dunnage material produced was generally used at the location of or in the immediate vincinity of the dunnage producing machine, and the transfer of the dunnage pad material to another location was not too convenient.